1 /* Chains of recurrences.
2 Copyright (C) 2003, 2004, 2005 Free Software Foundation, Inc.
3 Contributed by Sebastian Pop <s.pop@laposte.net>
5 This file is part of GCC.
7 GCC is free software; you can redistribute it and/or modify it under
8 the terms of the GNU General Public License as published by the Free
9 Software Foundation; either version 2, or (at your option) any later
12 GCC is distributed in the hope that it will be useful, but WITHOUT ANY
13 WARRANTY; without even the implied warranty of MERCHANTABILITY or
14 FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
17 You should have received a copy of the GNU General Public License
18 along with GCC; see the file COPYING. If not, write to the Free
19 Software Foundation, 51 Franklin Street, Fifth Floor, Boston, MA
22 /* This file implements operations on chains of recurrences. Chains
23 of recurrences are used for modeling evolution functions of scalar
29 #include "coretypes.h"
34 #include "diagnostic.h"
37 #include "tree-flow.h"
38 #include "tree-chrec.h"
39 #include "tree-pass.h"
44 /* Extended folder for chrecs. */
46 /* Determines whether CST is not a constant evolution. */
49 is_not_constant_evolution (tree cst)
51 return (TREE_CODE (cst) == POLYNOMIAL_CHREC);
54 /* Fold CODE for a polynomial function and a constant. */
57 chrec_fold_poly_cst (enum tree_code code,
64 gcc_assert (TREE_CODE (poly) == POLYNOMIAL_CHREC);
65 gcc_assert (!is_not_constant_evolution (cst));
70 return build_polynomial_chrec
71 (CHREC_VARIABLE (poly),
72 chrec_fold_plus (type, CHREC_LEFT (poly), cst),
76 return build_polynomial_chrec
77 (CHREC_VARIABLE (poly),
78 chrec_fold_minus (type, CHREC_LEFT (poly), cst),
82 return build_polynomial_chrec
83 (CHREC_VARIABLE (poly),
84 chrec_fold_multiply (type, CHREC_LEFT (poly), cst),
85 chrec_fold_multiply (type, CHREC_RIGHT (poly), cst));
88 return chrec_dont_know;
92 /* Fold the addition of two polynomial functions. */
95 chrec_fold_plus_poly_poly (enum tree_code code,
104 gcc_assert (TREE_CODE (poly0) == POLYNOMIAL_CHREC);
105 gcc_assert (TREE_CODE (poly1) == POLYNOMIAL_CHREC);
108 {a, +, b}_1 + {c, +, d}_2 -> {{a, +, b}_1 + c, +, d}_2,
109 {a, +, b}_2 + {c, +, d}_1 -> {{c, +, d}_1 + a, +, b}_2,
110 {a, +, b}_x + {c, +, d}_x -> {a+c, +, b+d}_x. */
111 if (CHREC_VARIABLE (poly0) < CHREC_VARIABLE (poly1))
113 if (code == PLUS_EXPR)
114 return build_polynomial_chrec
115 (CHREC_VARIABLE (poly1),
116 chrec_fold_plus (type, poly0, CHREC_LEFT (poly1)),
117 CHREC_RIGHT (poly1));
119 return build_polynomial_chrec
120 (CHREC_VARIABLE (poly1),
121 chrec_fold_minus (type, poly0, CHREC_LEFT (poly1)),
122 chrec_fold_multiply (type, CHREC_RIGHT (poly1),
123 SCALAR_FLOAT_TYPE_P (type)
124 ? build_real (type, dconstm1)
125 : build_int_cst_type (type, -1)));
128 if (CHREC_VARIABLE (poly0) > CHREC_VARIABLE (poly1))
130 if (code == PLUS_EXPR)
131 return build_polynomial_chrec
132 (CHREC_VARIABLE (poly0),
133 chrec_fold_plus (type, CHREC_LEFT (poly0), poly1),
134 CHREC_RIGHT (poly0));
136 return build_polynomial_chrec
137 (CHREC_VARIABLE (poly0),
138 chrec_fold_minus (type, CHREC_LEFT (poly0), poly1),
139 CHREC_RIGHT (poly0));
142 if (code == PLUS_EXPR)
144 left = chrec_fold_plus
145 (type, CHREC_LEFT (poly0), CHREC_LEFT (poly1));
146 right = chrec_fold_plus
147 (type, CHREC_RIGHT (poly0), CHREC_RIGHT (poly1));
151 left = chrec_fold_minus
152 (type, CHREC_LEFT (poly0), CHREC_LEFT (poly1));
153 right = chrec_fold_minus
154 (type, CHREC_RIGHT (poly0), CHREC_RIGHT (poly1));
157 if (chrec_zerop (right))
160 return build_polynomial_chrec
161 (CHREC_VARIABLE (poly0), left, right);
166 /* Fold the multiplication of two polynomial functions. */
169 chrec_fold_multiply_poly_poly (tree type,
178 gcc_assert (TREE_CODE (poly0) == POLYNOMIAL_CHREC);
179 gcc_assert (TREE_CODE (poly1) == POLYNOMIAL_CHREC);
181 /* {a, +, b}_1 * {c, +, d}_2 -> {c*{a, +, b}_1, +, d}_2,
182 {a, +, b}_2 * {c, +, d}_1 -> {a*{c, +, d}_1, +, b}_2,
183 {a, +, b}_x * {c, +, d}_x -> {a*c, +, a*d + b*c + b*d, +, 2*b*d}_x. */
184 if (CHREC_VARIABLE (poly0) < CHREC_VARIABLE (poly1))
185 /* poly0 is a constant wrt. poly1. */
186 return build_polynomial_chrec
187 (CHREC_VARIABLE (poly1),
188 chrec_fold_multiply (type, CHREC_LEFT (poly1), poly0),
189 CHREC_RIGHT (poly1));
191 if (CHREC_VARIABLE (poly1) < CHREC_VARIABLE (poly0))
192 /* poly1 is a constant wrt. poly0. */
193 return build_polynomial_chrec
194 (CHREC_VARIABLE (poly0),
195 chrec_fold_multiply (type, CHREC_LEFT (poly0), poly1),
196 CHREC_RIGHT (poly0));
198 /* poly0 and poly1 are two polynomials in the same variable,
199 {a, +, b}_x * {c, +, d}_x -> {a*c, +, a*d + b*c + b*d, +, 2*b*d}_x. */
202 t0 = chrec_fold_multiply (type, CHREC_LEFT (poly0), CHREC_LEFT (poly1));
204 /* "a*d + b*c + b*d". */
205 t1 = chrec_fold_multiply (type, CHREC_LEFT (poly0), CHREC_RIGHT (poly1));
206 t1 = chrec_fold_plus (type, t1, chrec_fold_multiply (type,
208 CHREC_LEFT (poly1)));
209 t1 = chrec_fold_plus (type, t1, chrec_fold_multiply (type,
211 CHREC_RIGHT (poly1)));
213 t2 = chrec_fold_multiply (type, CHREC_RIGHT (poly0), CHREC_RIGHT (poly1));
214 t2 = chrec_fold_multiply (type, SCALAR_FLOAT_TYPE_P (type)
215 ? build_real (type, dconst2)
216 : build_int_cst_type (type, 2), t2);
218 var = CHREC_VARIABLE (poly0);
219 return build_polynomial_chrec (var, t0,
220 build_polynomial_chrec (var, t1, t2));
223 /* When the operands are automatically_generated_chrec_p, the fold has
224 to respect the semantics of the operands. */
227 chrec_fold_automatically_generated_operands (tree op0,
230 if (op0 == chrec_dont_know
231 || op1 == chrec_dont_know)
232 return chrec_dont_know;
234 if (op0 == chrec_known
235 || op1 == chrec_known)
238 if (op0 == chrec_not_analyzed_yet
239 || op1 == chrec_not_analyzed_yet)
240 return chrec_not_analyzed_yet;
242 /* The default case produces a safe result. */
243 return chrec_dont_know;
246 /* Fold the addition of two chrecs. */
249 chrec_fold_plus_1 (enum tree_code code,
254 if (automatically_generated_chrec_p (op0)
255 || automatically_generated_chrec_p (op1))
256 return chrec_fold_automatically_generated_operands (op0, op1);
258 switch (TREE_CODE (op0))
260 case POLYNOMIAL_CHREC:
261 switch (TREE_CODE (op1))
263 case POLYNOMIAL_CHREC:
264 return chrec_fold_plus_poly_poly (code, type, op0, op1);
267 if (code == PLUS_EXPR)
268 return build_polynomial_chrec
269 (CHREC_VARIABLE (op0),
270 chrec_fold_plus (type, CHREC_LEFT (op0), op1),
273 return build_polynomial_chrec
274 (CHREC_VARIABLE (op0),
275 chrec_fold_minus (type, CHREC_LEFT (op0), op1),
280 switch (TREE_CODE (op1))
282 case POLYNOMIAL_CHREC:
283 if (code == PLUS_EXPR)
284 return build_polynomial_chrec
285 (CHREC_VARIABLE (op1),
286 chrec_fold_plus (type, op0, CHREC_LEFT (op1)),
289 return build_polynomial_chrec
290 (CHREC_VARIABLE (op1),
291 chrec_fold_minus (type, op0, CHREC_LEFT (op1)),
292 chrec_fold_multiply (type, CHREC_RIGHT (op1),
293 SCALAR_FLOAT_TYPE_P (type)
294 ? build_real (type, dconstm1)
295 : build_int_cst_type (type, -1)));
300 if ((tree_contains_chrecs (op0, &size)
301 || tree_contains_chrecs (op1, &size))
302 && size < PARAM_VALUE (PARAM_SCEV_MAX_EXPR_SIZE))
303 return build2 (code, type, op0, op1);
304 else if (size < PARAM_VALUE (PARAM_SCEV_MAX_EXPR_SIZE))
305 return fold_build2 (code, type,
306 fold_convert (type, op0),
307 fold_convert (type, op1));
309 return chrec_dont_know;
315 /* Fold the addition of two chrecs. */
318 chrec_fold_plus (tree type,
322 if (integer_zerop (op0))
324 if (integer_zerop (op1))
327 return chrec_fold_plus_1 (PLUS_EXPR, type, op0, op1);
330 /* Fold the subtraction of two chrecs. */
333 chrec_fold_minus (tree type,
337 if (integer_zerop (op1))
340 return chrec_fold_plus_1 (MINUS_EXPR, type, op0, op1);
343 /* Fold the multiplication of two chrecs. */
346 chrec_fold_multiply (tree type,
350 if (automatically_generated_chrec_p (op0)
351 || automatically_generated_chrec_p (op1))
352 return chrec_fold_automatically_generated_operands (op0, op1);
354 switch (TREE_CODE (op0))
356 case POLYNOMIAL_CHREC:
357 switch (TREE_CODE (op1))
359 case POLYNOMIAL_CHREC:
360 return chrec_fold_multiply_poly_poly (type, op0, op1);
363 if (integer_onep (op1))
365 if (integer_zerop (op1))
366 return build_int_cst_type (type, 0);
368 return build_polynomial_chrec
369 (CHREC_VARIABLE (op0),
370 chrec_fold_multiply (type, CHREC_LEFT (op0), op1),
371 chrec_fold_multiply (type, CHREC_RIGHT (op0), op1));
375 if (integer_onep (op0))
378 if (integer_zerop (op0))
379 return build_int_cst_type (type, 0);
381 switch (TREE_CODE (op1))
383 case POLYNOMIAL_CHREC:
384 return build_polynomial_chrec
385 (CHREC_VARIABLE (op1),
386 chrec_fold_multiply (type, CHREC_LEFT (op1), op0),
387 chrec_fold_multiply (type, CHREC_RIGHT (op1), op0));
390 if (integer_onep (op1))
392 if (integer_zerop (op1))
393 return build_int_cst_type (type, 0);
394 return fold_build2 (MULT_EXPR, type, op0, op1);
403 /* Evaluate the binomial coefficient. Return NULL_TREE if the intermediate
404 calculation overflows, otherwise return C(n,k) with type TYPE. */
407 tree_fold_binomial (tree type, tree n, unsigned int k)
409 unsigned HOST_WIDE_INT lidx, lnum, ldenom, lres, ldum;
410 HOST_WIDE_INT hidx, hnum, hdenom, hres, hdum;
414 /* Handle the most frequent cases. */
416 return build_int_cst (type, 1);
418 return fold_convert (type, n);
420 /* Check that k <= n. */
421 if (TREE_INT_CST_HIGH (n) == 0
422 && TREE_INT_CST_LOW (n) < k)
426 lnum = TREE_INT_CST_LOW (n);
427 hnum = TREE_INT_CST_HIGH (n);
429 /* Denominator = 2. */
433 /* Index = Numerator-1. */
437 lidx = ~ (unsigned HOST_WIDE_INT) 0;
445 /* Numerator = Numerator*Index = n*(n-1). */
446 if (mul_double (lnum, hnum, lidx, hidx, &lnum, &hnum))
449 for (i = 3; i <= k; i++)
455 lidx = ~ (unsigned HOST_WIDE_INT) 0;
460 /* Numerator *= Index. */
461 if (mul_double (lnum, hnum, lidx, hidx, &lnum, &hnum))
464 /* Denominator *= i. */
465 mul_double (ldenom, hdenom, i, 0, &ldenom, &hdenom);
468 /* Result = Numerator / Denominator. */
469 div_and_round_double (EXACT_DIV_EXPR, 1, lnum, hnum, ldenom, hdenom,
470 &lres, &hres, &ldum, &hdum);
472 res = build_int_cst_wide (type, lres, hres);
473 return int_fits_type_p (res, type) ? res : NULL_TREE;
476 /* Helper function. Use the Newton's interpolating formula for
477 evaluating the value of the evolution function. */
480 chrec_evaluate (unsigned var, tree chrec, tree n, unsigned int k)
482 tree arg0, arg1, binomial_n_k;
483 tree type = TREE_TYPE (chrec);
485 while (TREE_CODE (chrec) == POLYNOMIAL_CHREC
486 && CHREC_VARIABLE (chrec) > var)
487 chrec = CHREC_LEFT (chrec);
489 if (TREE_CODE (chrec) == POLYNOMIAL_CHREC
490 && CHREC_VARIABLE (chrec) == var)
492 arg0 = chrec_evaluate (var, CHREC_RIGHT (chrec), n, k + 1);
493 if (arg0 == chrec_dont_know)
494 return chrec_dont_know;
495 binomial_n_k = tree_fold_binomial (type, n, k);
497 return chrec_dont_know;
498 arg1 = fold_build2 (MULT_EXPR, type,
499 CHREC_LEFT (chrec), binomial_n_k);
500 return chrec_fold_plus (type, arg0, arg1);
503 binomial_n_k = tree_fold_binomial (type, n, k);
505 return chrec_dont_know;
507 return fold_build2 (MULT_EXPR, type, chrec, binomial_n_k);
510 /* Evaluates "CHREC (X)" when the varying variable is VAR.
511 Example: Given the following parameters,
517 The result is given by the Newton's interpolating formula:
518 3 * \binom{10}{0} + 4 * \binom{10}{1}.
522 chrec_apply (unsigned var,
526 tree type = chrec_type (chrec);
527 tree res = chrec_dont_know;
529 if (automatically_generated_chrec_p (chrec)
530 || automatically_generated_chrec_p (x)
532 /* When the symbols are defined in an outer loop, it is possible
533 to symbolically compute the apply, since the symbols are
534 constants with respect to the varying loop. */
535 || chrec_contains_symbols_defined_in_loop (chrec, var)
536 || chrec_contains_symbols (x))
537 return chrec_dont_know;
539 if (dump_file && (dump_flags & TDF_DETAILS))
540 fprintf (dump_file, "(chrec_apply \n");
542 if (TREE_CODE (x) == INTEGER_CST && SCALAR_FLOAT_TYPE_P (type))
543 x = build_real_from_int_cst (type, x);
545 if (evolution_function_is_affine_p (chrec))
547 /* "{a, +, b} (x)" -> "a + b*x". */
548 if (TREE_CODE (CHREC_LEFT (chrec)) == INTEGER_CST
549 && integer_zerop (CHREC_LEFT (chrec)))
550 res = chrec_fold_multiply (type, CHREC_RIGHT (chrec), x);
553 res = chrec_fold_plus (type, CHREC_LEFT (chrec),
554 chrec_fold_multiply (type,
555 CHREC_RIGHT (chrec), x));
558 else if (TREE_CODE (chrec) != POLYNOMIAL_CHREC)
561 else if (TREE_CODE (x) == INTEGER_CST
562 && tree_int_cst_sgn (x) == 1)
563 /* testsuite/.../ssa-chrec-38.c. */
564 res = chrec_evaluate (var, chrec, x, 0);
567 res = chrec_dont_know;
569 if (dump_file && (dump_flags & TDF_DETAILS))
571 fprintf (dump_file, " (varying_loop = %d\n", var);
572 fprintf (dump_file, ")\n (chrec = ");
573 print_generic_expr (dump_file, chrec, 0);
574 fprintf (dump_file, ")\n (x = ");
575 print_generic_expr (dump_file, x, 0);
576 fprintf (dump_file, ")\n (res = ");
577 print_generic_expr (dump_file, res, 0);
578 fprintf (dump_file, "))\n");
584 /* Replaces the initial condition in CHREC with INIT_COND. */
587 chrec_replace_initial_condition (tree chrec,
590 if (automatically_generated_chrec_p (chrec))
593 switch (TREE_CODE (chrec))
595 case POLYNOMIAL_CHREC:
596 return build_polynomial_chrec
597 (CHREC_VARIABLE (chrec),
598 chrec_replace_initial_condition (CHREC_LEFT (chrec), init_cond),
599 CHREC_RIGHT (chrec));
606 /* Returns the initial condition of a given CHREC. */
609 initial_condition (tree chrec)
611 if (automatically_generated_chrec_p (chrec))
614 if (TREE_CODE (chrec) == POLYNOMIAL_CHREC)
615 return initial_condition (CHREC_LEFT (chrec));
620 /* Returns a univariate function that represents the evolution in
621 LOOP_NUM. Mask the evolution of any other loop. */
624 hide_evolution_in_other_loops_than_loop (tree chrec,
627 if (automatically_generated_chrec_p (chrec))
630 switch (TREE_CODE (chrec))
632 case POLYNOMIAL_CHREC:
633 if (CHREC_VARIABLE (chrec) == loop_num)
634 return build_polynomial_chrec
636 hide_evolution_in_other_loops_than_loop (CHREC_LEFT (chrec),
638 CHREC_RIGHT (chrec));
640 else if (CHREC_VARIABLE (chrec) < loop_num)
641 /* There is no evolution in this loop. */
642 return initial_condition (chrec);
645 return hide_evolution_in_other_loops_than_loop (CHREC_LEFT (chrec),
653 /* Returns the evolution part of CHREC in LOOP_NUM when RIGHT is
654 true, otherwise returns the initial condition in LOOP_NUM. */
657 chrec_component_in_loop_num (tree chrec,
663 if (automatically_generated_chrec_p (chrec))
666 switch (TREE_CODE (chrec))
668 case POLYNOMIAL_CHREC:
669 if (CHREC_VARIABLE (chrec) == loop_num)
672 component = CHREC_RIGHT (chrec);
674 component = CHREC_LEFT (chrec);
676 if (TREE_CODE (CHREC_LEFT (chrec)) != POLYNOMIAL_CHREC
677 || CHREC_VARIABLE (CHREC_LEFT (chrec)) != CHREC_VARIABLE (chrec))
681 return build_polynomial_chrec
683 chrec_component_in_loop_num (CHREC_LEFT (chrec),
689 else if (CHREC_VARIABLE (chrec) < loop_num)
690 /* There is no evolution part in this loop. */
694 return chrec_component_in_loop_num (CHREC_LEFT (chrec),
706 /* Returns the evolution part in LOOP_NUM. Example: the call
707 evolution_part_in_loop_num ({{0, +, 1}_1, +, 2}_1, 1) returns
711 evolution_part_in_loop_num (tree chrec,
714 return chrec_component_in_loop_num (chrec, loop_num, true);
717 /* Returns the initial condition in LOOP_NUM. Example: the call
718 initial_condition_in_loop_num ({{0, +, 1}_1, +, 2}_2, 2) returns
722 initial_condition_in_loop_num (tree chrec,
725 return chrec_component_in_loop_num (chrec, loop_num, false);
728 /* Set or reset the evolution of CHREC to NEW_EVOL in loop LOOP_NUM.
729 This function is essentially used for setting the evolution to
730 chrec_dont_know, for example after having determined that it is
731 impossible to say how many times a loop will execute. */
734 reset_evolution_in_loop (unsigned loop_num,
738 if (TREE_CODE (chrec) == POLYNOMIAL_CHREC
739 && CHREC_VARIABLE (chrec) > loop_num)
741 tree left = reset_evolution_in_loop (loop_num, CHREC_LEFT (chrec),
743 tree right = reset_evolution_in_loop (loop_num, CHREC_RIGHT (chrec),
745 return build3 (POLYNOMIAL_CHREC, TREE_TYPE (left),
746 build_int_cst (NULL_TREE, CHREC_VARIABLE (chrec)),
750 while (TREE_CODE (chrec) == POLYNOMIAL_CHREC
751 && CHREC_VARIABLE (chrec) == loop_num)
752 chrec = CHREC_LEFT (chrec);
754 return build_polynomial_chrec (loop_num, chrec, new_evol);
757 /* Merges two evolution functions that were found by following two
758 alternate paths of a conditional expression. */
761 chrec_merge (tree chrec1,
764 if (chrec1 == chrec_dont_know
765 || chrec2 == chrec_dont_know)
766 return chrec_dont_know;
768 if (chrec1 == chrec_known
769 || chrec2 == chrec_known)
772 if (chrec1 == chrec_not_analyzed_yet)
774 if (chrec2 == chrec_not_analyzed_yet)
777 if (operand_equal_p (chrec1, chrec2, 0))
780 return chrec_dont_know;
787 /* Helper function for is_multivariate_chrec. */
790 is_multivariate_chrec_rec (tree chrec, unsigned int rec_var)
792 if (chrec == NULL_TREE)
795 if (TREE_CODE (chrec) == POLYNOMIAL_CHREC)
797 if (CHREC_VARIABLE (chrec) != rec_var)
800 return (is_multivariate_chrec_rec (CHREC_LEFT (chrec), rec_var)
801 || is_multivariate_chrec_rec (CHREC_RIGHT (chrec), rec_var));
807 /* Determine whether the given chrec is multivariate or not. */
810 is_multivariate_chrec (tree chrec)
812 if (chrec == NULL_TREE)
815 if (TREE_CODE (chrec) == POLYNOMIAL_CHREC)
816 return (is_multivariate_chrec_rec (CHREC_LEFT (chrec),
817 CHREC_VARIABLE (chrec))
818 || is_multivariate_chrec_rec (CHREC_RIGHT (chrec),
819 CHREC_VARIABLE (chrec)));
824 /* Determines whether the chrec contains symbolic names or not. */
827 chrec_contains_symbols (tree chrec)
829 if (chrec == NULL_TREE)
832 if (TREE_CODE (chrec) == SSA_NAME
833 || TREE_CODE (chrec) == VAR_DECL
834 || TREE_CODE (chrec) == PARM_DECL
835 || TREE_CODE (chrec) == FUNCTION_DECL
836 || TREE_CODE (chrec) == LABEL_DECL
837 || TREE_CODE (chrec) == RESULT_DECL
838 || TREE_CODE (chrec) == FIELD_DECL)
841 switch (TREE_CODE_LENGTH (TREE_CODE (chrec)))
844 if (chrec_contains_symbols (TREE_OPERAND (chrec, 2)))
848 if (chrec_contains_symbols (TREE_OPERAND (chrec, 1)))
852 if (chrec_contains_symbols (TREE_OPERAND (chrec, 0)))
860 /* Determines whether the chrec contains undetermined coefficients. */
863 chrec_contains_undetermined (tree chrec)
865 if (chrec == chrec_dont_know
866 || chrec == chrec_not_analyzed_yet
867 || chrec == NULL_TREE)
870 switch (TREE_CODE_LENGTH (TREE_CODE (chrec)))
873 if (chrec_contains_undetermined (TREE_OPERAND (chrec, 2)))
877 if (chrec_contains_undetermined (TREE_OPERAND (chrec, 1)))
881 if (chrec_contains_undetermined (TREE_OPERAND (chrec, 0)))
889 /* Determines whether the tree EXPR contains chrecs, and increment
890 SIZE if it is not a NULL pointer by an estimation of the depth of
894 tree_contains_chrecs (tree expr, int *size)
896 if (expr == NULL_TREE)
902 if (tree_is_chrec (expr))
905 switch (TREE_CODE_LENGTH (TREE_CODE (expr)))
908 if (tree_contains_chrecs (TREE_OPERAND (expr, 2), size))
912 if (tree_contains_chrecs (TREE_OPERAND (expr, 1), size))
916 if (tree_contains_chrecs (TREE_OPERAND (expr, 0), size))
924 /* Recursive helper function. */
927 evolution_function_is_invariant_rec_p (tree chrec, int loopnum)
929 if (evolution_function_is_constant_p (chrec))
932 if (TREE_CODE (chrec) == SSA_NAME
933 && expr_invariant_in_loop_p (current_loops->parray[loopnum],
937 if (TREE_CODE (chrec) == POLYNOMIAL_CHREC
938 && CHREC_VARIABLE (chrec) == (unsigned) loopnum)
941 switch (TREE_CODE_LENGTH (TREE_CODE (chrec)))
944 if (!evolution_function_is_invariant_rec_p (TREE_OPERAND (chrec, 1),
949 if (!evolution_function_is_invariant_rec_p (TREE_OPERAND (chrec, 0),
961 /* Return true if CHREC is invariant in loop LOOPNUM, false otherwise. */
964 evolution_function_is_invariant_p (tree chrec, int loopnum)
966 if (evolution_function_is_constant_p (chrec))
969 if (current_loops != NULL)
970 return evolution_function_is_invariant_rec_p (chrec, loopnum);
975 /* Determine whether the given tree is an affine multivariate
979 evolution_function_is_affine_multivariate_p (tree chrec)
981 if (chrec == NULL_TREE)
984 switch (TREE_CODE (chrec))
986 case POLYNOMIAL_CHREC:
987 if (evolution_function_is_constant_p (CHREC_LEFT (chrec)))
989 if (evolution_function_is_constant_p (CHREC_RIGHT (chrec)))
993 if (TREE_CODE (CHREC_RIGHT (chrec)) == POLYNOMIAL_CHREC
994 && CHREC_VARIABLE (CHREC_RIGHT (chrec))
995 != CHREC_VARIABLE (chrec)
996 && evolution_function_is_affine_multivariate_p
997 (CHREC_RIGHT (chrec)))
1005 if (evolution_function_is_constant_p (CHREC_RIGHT (chrec))
1006 && TREE_CODE (CHREC_LEFT (chrec)) == POLYNOMIAL_CHREC
1007 && CHREC_VARIABLE (CHREC_LEFT (chrec)) != CHREC_VARIABLE (chrec)
1008 && evolution_function_is_affine_multivariate_p
1009 (CHREC_LEFT (chrec)))
1020 /* Determine whether the given tree is a function in zero or one
1024 evolution_function_is_univariate_p (tree chrec)
1026 if (chrec == NULL_TREE)
1029 switch (TREE_CODE (chrec))
1031 case POLYNOMIAL_CHREC:
1032 switch (TREE_CODE (CHREC_LEFT (chrec)))
1034 case POLYNOMIAL_CHREC:
1035 if (CHREC_VARIABLE (chrec) != CHREC_VARIABLE (CHREC_LEFT (chrec)))
1037 if (!evolution_function_is_univariate_p (CHREC_LEFT (chrec)))
1045 switch (TREE_CODE (CHREC_RIGHT (chrec)))
1047 case POLYNOMIAL_CHREC:
1048 if (CHREC_VARIABLE (chrec) != CHREC_VARIABLE (CHREC_RIGHT (chrec)))
1050 if (!evolution_function_is_univariate_p (CHREC_RIGHT (chrec)))
1063 /* Returns the number of variables of CHREC. Example: the call
1064 nb_vars_in_chrec ({{0, +, 1}_5, +, 2}_6) returns 2. */
1067 nb_vars_in_chrec (tree chrec)
1069 if (chrec == NULL_TREE)
1072 switch (TREE_CODE (chrec))
1074 case POLYNOMIAL_CHREC:
1075 return 1 + nb_vars_in_chrec
1076 (initial_condition_in_loop_num (chrec, CHREC_VARIABLE (chrec)));
1085 /* Convert CHREC to TYPE. When the analyzer knows the context in
1086 which the CHREC is built, it sets AT_STMT to the statement that
1087 contains the definition of the analyzed variable, otherwise the
1088 conversion is less accurate: the information is used for
1089 determining a more accurate estimation of the number of iterations.
1090 By default AT_STMT could be safely set to NULL_TREE.
1092 The following rule is always true: TREE_TYPE (chrec) ==
1093 TREE_TYPE (CHREC_LEFT (chrec)) == TREE_TYPE (CHREC_RIGHT (chrec)).
1094 An example of what could happen when adding two chrecs and the type
1095 of the CHREC_RIGHT is different than CHREC_LEFT is:
1097 {(uint) 0, +, (uchar) 10} +
1098 {(uint) 0, +, (uchar) 250}
1100 that would produce a wrong result if CHREC_RIGHT is not (uint):
1102 {(uint) 0, +, (uchar) 4}
1106 {(uint) 0, +, (uint) 260}
1110 chrec_convert (tree type, tree chrec, tree at_stmt)
1114 if (automatically_generated_chrec_p (chrec))
1117 ct = chrec_type (chrec);
1121 if (evolution_function_is_affine_p (chrec))
1126 /* Avoid conversion of (signed char) {(uchar)1, +, (uchar)1}_x
1127 when it is not possible to prove that the scev does not wrap.
1128 See PR22236, where a sequence 1, 2, ..., 255 has to be
1129 converted to signed char, but this would wrap:
1130 1, 2, ..., 127, -128, ... The result should not be
1131 {(schar)1, +, (schar)1}_x, but instead, we should keep the
1132 conversion: (schar) {(uchar)1, +, (uchar)1}_x. */
1133 if (scev_probably_wraps_p (type, CHREC_LEFT (chrec), CHREC_RIGHT (chrec),
1135 current_loops->parray[CHREC_VARIABLE (chrec)],
1137 return fold_convert (type, chrec);
1139 step = convert_step (current_loops->parray[CHREC_VARIABLE (chrec)], type,
1140 CHREC_LEFT (chrec), CHREC_RIGHT (chrec), at_stmt);
1142 return fold_convert (type, chrec);
1144 return build_polynomial_chrec (CHREC_VARIABLE (chrec),
1145 chrec_convert (type, CHREC_LEFT (chrec),
1150 if (TREE_CODE (chrec) == POLYNOMIAL_CHREC)
1151 return chrec_dont_know;
1153 res = fold_convert (type, chrec);
1155 /* Don't propagate overflows. */
1156 if (CONSTANT_CLASS_P (res))
1158 TREE_CONSTANT_OVERFLOW (res) = 0;
1159 TREE_OVERFLOW (res) = 0;
1162 /* But reject constants that don't fit in their type after conversion.
1163 This can happen if TYPE_MIN_VALUE or TYPE_MAX_VALUE are not the
1164 natural values associated with TYPE_PRECISION and TYPE_UNSIGNED,
1165 and can cause problems later when computing niters of loops. Note
1166 that we don't do the check before converting because we don't want
1167 to reject conversions of negative chrecs to unsigned types. */
1168 if (TREE_CODE (res) == INTEGER_CST
1169 && TREE_CODE (type) == INTEGER_TYPE
1170 && !int_fits_type_p (res, type))
1171 res = chrec_dont_know;
1176 /* Returns the type of the chrec. */
1179 chrec_type (tree chrec)
1181 if (automatically_generated_chrec_p (chrec))
1184 return TREE_TYPE (chrec);